Bodyfat Comparisons

plot(BodyFat$WEIGHT, BodyFat$BODYFAT, main="BodyFat % by Weight",
   xlab="Weight", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$WEIGHT), col="red")

summary(model1 <- lm(BodyFat$BODYFAT~BodyFat$WEIGHT))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$WEIGHT)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.3283  -4.2438  -0.0054   4.4562  19.8010 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    -9.06248    2.41993  -3.745 0.000224 ***
## BodyFat$WEIGHT  0.15690    0.01332  11.781  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.107 on 248 degrees of freedom
## Multiple R-squared:  0.3588, Adjusted R-squared:  0.3563 
## F-statistic: 138.8 on 1 and 248 DF,  p-value: < 2.2e-16
res1 <- resid(model1)
plot(fitted(model1), res1)
abline(0,0)

plot(BodyFat$Neck.Inch., BodyFat$BODYFAT, main="BodyFat % by Neck",
   xlab="Neck Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Neck.Inch.), col="red")

summary(model2 <- lm(BodyFat$BODYFAT~BodyFat$Neck.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Neck.Inch.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.0953  -4.8309  -0.2711   5.0044  21.2513 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        -37.9965     6.7130   -5.66 4.17e-08 ***
## BodyFat$Neck.Inch.   3.8128     0.4475    8.52 1.57e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.708 on 248 degrees of freedom
## Multiple R-squared:  0.2264, Adjusted R-squared:  0.2233 
## F-statistic: 72.59 on 1 and 248 DF,  p-value: 1.569e-15
res2 <- resid(model2)
plot(fitted(model2), res2)
abline(0,0)

plot(BodyFat$Chest.Inch., BodyFat$BODYFAT, main="BodyFat % by Chest",
   xlab="Chest Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Chest.Inch.), col="red")

summary(model3 <- lm(BodyFat$BODYFAT~BodyFat$Chest.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Chest.Inch.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.9505  -3.8506  -0.3307   3.4779  14.0724 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -44.8911     4.2353  -10.60   <2e-16 ***
## BodyFat$Chest.Inch.   1.6096     0.1062   15.16   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.495 on 248 degrees of freedom
## Multiple R-squared:  0.4808, Adjusted R-squared:  0.4787 
## F-statistic: 229.7 on 1 and 248 DF,  p-value: < 2.2e-16
res3 <- resid(model3)
plot(fitted(model3), res3)
abline(0,0)

plot(BodyFat$Abdomen.Inch., BodyFat$BODYFAT, main="BodyFat % by Abdomen",
   xlab="Abdomen Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Abdomen.Inch.), col="red")

summary(model4 <- lm(BodyFat$BODYFAT~BodyFat$Abdomen.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Abdomen.Inch.)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -17.194  -3.514  -0.054   3.003  11.937 
## 
## Coefficients:
##                        Estimate Std. Error t value Pr(>|t|)    
## (Intercept)           -34.34373    2.49383  -13.77   <2e-16 ***
## BodyFat$Abdomen.Inch.   1.46359    0.06787   21.56   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.498 on 248 degrees of freedom
## Multiple R-squared:  0.6522, Adjusted R-squared:  0.6508 
## F-statistic:   465 on 1 and 248 DF,  p-value: < 2.2e-16
res4 <- resid(model4)
plot(fitted(model4), res4)
abline(0,0)

plot(BodyFat$Hip.Inch., BodyFat$BODYFAT, main="BodyFat % by Hip",
   xlab="Hip Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Hip.Inch.), col="red")

summary(model5 <- lm(BodyFat$BODYFAT~BodyFat$Hip.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Hip.Inch.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.6607  -3.6312  -0.1486   4.2709  17.6009 
## 
## Coefficients:
##                   Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       -46.7149     5.3914  -8.665 5.94e-16 ***
## BodyFat$Hip.Inch.   1.6711     0.1366  12.235  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.023 on 248 degrees of freedom
## Multiple R-squared:  0.3764, Adjusted R-squared:  0.3739 
## F-statistic: 149.7 on 1 and 248 DF,  p-value: < 2.2e-16
res5 <- resid(model5)
plot(fitted(model5), res5)
abline(0,0)

plot(BodyFat$Thigh.Inch., BodyFat$BODYFAT, main="BodyFat % by Thigh",
   xlab="Thigh Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Thigh.Inch.), col="red")

summary(model6 <- lm(BodyFat$BODYFAT~BodyFat$Thigh.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Thigh.Inch.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -16.7060  -4.3158  -0.0381   4.2817  23.6137 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -28.4688     4.6766  -6.088 4.33e-09 ***
## BodyFat$Thigh.Inch.   2.0302     0.1989  10.206  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.4 on 248 degrees of freedom
## Multiple R-squared:  0.2958, Adjusted R-squared:  0.293 
## F-statistic: 104.2 on 1 and 248 DF,  p-value: < 2.2e-16
res6 <- resid(model6)
plot(fitted(model6), res6)
abline(0,0)

plot(BodyFat$Wrist.Inch , BodyFat$BODYFAT, main="BodyFat % by Wrist",
   xlab="Wrist Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Wrist.Inch.), col="red")

summary(model15 <- lm(BodyFat$BODYFAT~BodyFat$Wrist.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Wrist.Inch.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.8762  -5.5830   0.0975   4.9789  25.5927 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -29.976      8.998  -3.331 0.000996 ***
## BodyFat$Wrist.Inch.    6.831      1.251   5.459 1.16e-07 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 7.206 on 248 degrees of freedom
## Multiple R-squared:  0.1073, Adjusted R-squared:  0.1037 
## F-statistic:  29.8 on 1 and 248 DF,  p-value: 1.16e-07
res15 <- resid(model15)
plot(fitted(model15), res15)
abline(0,0)

print(cor(BodyFat$BODYFAT,BodyFat$Wrist.Inch.))
## [1] 0.3275347
plot(BodyFat$Knee.Inch , BodyFat$BODYFAT, main="BodyFat % by Knee",
   xlab="Knee Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Knee.Inch.), col="red")

summary(model16 <- lm(BodyFat$BODYFAT~BodyFat$Knee.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Knee.Inch.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.9317  -4.4330  -0.2264   3.8845  28.7175 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         -41.338      6.826  -6.056 5.14e-09 ***
## BodyFat$Knee.Inch.    3.973      0.448   8.868  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.645 on 248 degrees of freedom
## Multiple R-squared:  0.2408, Adjusted R-squared:  0.2377 
## F-statistic: 78.65 on 1 and 248 DF,  p-value: < 2.2e-16
res16 <- resid(model16)
plot(fitted(model16), res16)
abline(0,0)

print(cor(BodyFat$BODYFAT,BodyFat$Knee.Inch.))
## [1] 0.4906831
plot(BodyFat$Biceps.Inch , BodyFat$BODYFAT, main="BodyFat % by Bicep",
   xlab="Bicep Circ.", ylab="BodyFat %", pch=19)
abline(lm(BodyFat$BODYFAT~BodyFat$Biceps.Inch.), col="red")

summary(model17 <- lm(BodyFat$BODYFAT~BodyFat$Biceps.Inch.))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$Biceps.Inch.)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -19.4682  -5.0161   0.0371   4.6889  23.1359 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          -20.0785     4.6308  -4.336 2.11e-05 ***
## BodyFat$Biceps.Inch.   3.0775     0.3624   8.492 1.88e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.713 on 248 degrees of freedom
## Multiple R-squared:  0.2253, Adjusted R-squared:  0.2222 
## F-statistic: 72.12 on 1 and 248 DF,  p-value: 1.885e-15
res17 <- resid(model17)
plot(fitted(model17), res17)
abline(0,0)

print(cor(BodyFat$BODYFAT,BodyFat$Biceps.Inch.))
## [1] 0.4746496

Density Comparisons

plot(BodyFat$WEIGHT, BodyFat$DENSITY, main="Density by Weight",
   xlab="Weight", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$WEIGHT), col="red")

summary(model7 <- lm(BodyFat$DENSITY~BodyFat$WEIGHT))
## 
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$WEIGHT)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.045518 -0.011178 -0.000312  0.009787  0.060619 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     1.122e+00  6.027e-03  186.09   <2e-16 ***
## BodyFat$WEIGHT -3.703e-04  3.317e-05  -11.16   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01521 on 248 degrees of freedom
## Multiple R-squared:  0.3345, Adjusted R-squared:  0.3318 
## F-statistic: 124.6 on 1 and 248 DF,  p-value: < 2.2e-16
res7 <- resid(model7)
plot(fitted(model7), res7)
abline(0,0)

plot(BodyFat$Neck.Inch., BodyFat$DENSITY, main="Density by Neck",
   xlab="Neck Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Neck.Inch.), col="red")

summary(model8 <- lm(BodyFat$DENSITY~BodyFat$Neck.Inch.))
## 
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Neck.Inch.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.049029 -0.012422  0.000111  0.011418  0.054720 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)         1.188848   0.016607  71.585  < 2e-16 ***
## BodyFat$Neck.Inch. -0.008928   0.001107  -8.064 3.15e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01659 on 248 degrees of freedom
## Multiple R-squared:  0.2077, Adjusted R-squared:  0.2046 
## F-statistic: 65.03 on 1 and 248 DF,  p-value: 3.149e-14
res8 <- resid(model8)
plot(fitted(model8), res8)
abline(0,0)

plot(BodyFat$Chest.Inch., BodyFat$DENSITY, main="Density by Chest",
   xlab="Chest Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Chest.Inch.), col="red")

summary(model9 <- lm(BodyFat$DENSITY~BodyFat$Chest.Inch.))
## 
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Chest.Inch.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.031922 -0.008539  0.000361  0.009136  0.062280 
## 
## Coefficients:
##                       Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          1.2065784  0.0106513  113.28   <2e-16 ***
## BodyFat$Chest.Inch. -0.0038091  0.0002671  -14.26   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01382 on 248 degrees of freedom
## Multiple R-squared:  0.4506, Adjusted R-squared:  0.4484 
## F-statistic: 203.4 on 1 and 248 DF,  p-value: < 2.2e-16
res9 <- resid(model9)
plot(fitted(model9), res9)
abline(0,0)

plot(BodyFat$Abdomen.Inch., BodyFat$DENSITY, main="Density by Abdomen",
   xlab="Abdomen Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Abdomen.Inch.), col="red")

summary(model10 <- lm(BodyFat$DENSITY~BodyFat$Abdomen.Inch.))
## 
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Abdomen.Inch.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.028557 -0.007219 -0.000409  0.008288  0.052866 
## 
## Coefficients:
##                         Estimate Std. Error t value Pr(>|t|)    
## (Intercept)            1.1833131  0.0063080  187.59   <2e-16 ***
## BodyFat$Abdomen.Inch. -0.0035099  0.0001717  -20.45   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01138 on 248 degrees of freedom
## Multiple R-squared:  0.6276, Adjusted R-squared:  0.6261 
## F-statistic:   418 on 1 and 248 DF,  p-value: < 2.2e-16
res10 <- resid(model10)
plot(fitted(model10), res10)
abline(0,0)

plot(BodyFat$Hip.Inch., BodyFat$DENSITY, main="Density by Hip",
   xlab="Hip Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Hip.Inch.), col="red")

summary(model11 <- lm(BodyFat$DENSITY~BodyFat$Hip.Inch.))
## 
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Hip.Inch.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.040209 -0.010954  0.000160  0.008383  0.055613 
## 
## Coefficients:
##                     Estimate Std. Error t value Pr(>|t|)    
## (Intercept)        1.2113887  0.0134047   90.37   <2e-16 ***
## BodyFat$Hip.Inch. -0.0039672  0.0003396  -11.68   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01497 on 248 degrees of freedom
## Multiple R-squared:  0.3549, Adjusted R-squared:  0.3523 
## F-statistic: 136.5 on 1 and 248 DF,  p-value: < 2.2e-16
res11 <- resid(model11)
plot(fitted(model11), res11)
abline(0,0)

plot(BodyFat$Thigh.Inch., BodyFat$DENSITY, main="Density by Thigh",
   xlab="Thigh Circ.", ylab="Density", pch=19)
abline(lm(BodyFat$DENSITY~BodyFat$Thigh.Inch.), col="red")

summary(model12 <- lm(BodyFat$DENSITY~BodyFat$Thigh.Inch.))
## 
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$Thigh.Inch.)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.054421 -0.010793 -0.000279  0.010415  0.048144 
## 
## Coefficients:
##                      Estimate Std. Error t value Pr(>|t|)    
## (Intercept)          1.169294   0.011520 101.504   <2e-16 ***
## BodyFat$Thigh.Inch. -0.004872   0.000490  -9.942   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01576 on 248 degrees of freedom
## Multiple R-squared:  0.285,  Adjusted R-squared:  0.2821 
## F-statistic: 98.85 on 1 and 248 DF,  p-value: < 2.2e-16
res12 <- resid(model12)
plot(fitted(model12), res12)
abline(0,0)

Height and Weight Combo

summary(model13 <- lm(BodyFat$BODYFAT~BodyFat$WEIGHT + BodyFat$HEIGHT))
## 
## Call:
## lm(formula = BodyFat$BODYFAT ~ BodyFat$WEIGHT + BodyFat$HEIGHT)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -21.6967  -3.3238  -0.0994   4.1984  12.2339 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    71.10432    9.58382   7.419 1.89e-12 ***
## BodyFat$WEIGHT  0.21147    0.01333  15.866  < 2e-16 ***
## BodyFat$HEIGHT -1.27895    0.14908  -8.579 1.07e-15 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.371 on 247 degrees of freedom
## Multiple R-squared:  0.506,  Adjusted R-squared:  0.502 
## F-statistic: 126.5 on 2 and 247 DF,  p-value: < 2.2e-16
res13 <- resid(model13)
plot(fitted(model13), res13)
abline(0,0)

summary(model14 <- lm(BodyFat$DENSITY~BodyFat$WEIGHT + BodyFat$HEIGHT))
## 
## Call:
## lm(formula = BodyFat$DENSITY ~ BodyFat$WEIGHT + BodyFat$HEIGHT)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.030154 -0.010359 -0.000209  0.007843  0.051994 
## 
## Coefficients:
##                  Estimate Std. Error t value Pr(>|t|)    
## (Intercept)     9.214e-01  2.385e-02   38.63  < 2e-16 ***
## BodyFat$WEIGHT -5.066e-04  3.317e-05  -15.27  < 2e-16 ***
## BodyFat$HEIGHT  3.194e-03  3.710e-04    8.61 8.73e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.01337 on 247 degrees of freedom
## Multiple R-squared:  0.4881, Adjusted R-squared:  0.484 
## F-statistic: 117.8 on 2 and 247 DF,  p-value: < 2.2e-16
res14 <- resid(model14)
plot(fitted(model14), res14)
abline(0,0)

All correlations

par(mfrow=c(4,3))
##scatter plot
print("Density Correlation:")
## [1] "Density Correlation:"
plot(BodyFat$DENSITY,BodyFat$BODYFAT)
cor(BodyFat$DENSITY,BodyFat$BODYFAT)
## [1] -0.9877761
print("Weight Correlation:")
## [1] "Weight Correlation:"
plot(BodyFat$WEIGHT,BodyFat$BODYFAT)
cor(BodyFat$WEIGHT,BodyFat$BODYFAT)
## [1] 0.5990389
print("Neck Correlation:")
## [1] "Neck Correlation:"
plot(BodyFat$Neck.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Neck.Inch.,BodyFat$BODYFAT)
## [1] 0.4758356
print("Chest Correlation:")
## [1] "Chest Correlation:"
plot(BodyFat$Chest.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Chest.Inch.,BodyFat$BODYFAT)
## [1] 0.6934283
print("DAbdomen Correlation:")
## [1] "DAbdomen Correlation:"
plot(BodyFat$Abdomen.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Abdomen.Inch.,BodyFat$BODYFAT)
## [1] 0.8075761
print("Hip Correlation:")
## [1] "Hip Correlation:"
plot(BodyFat$Hip.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Hip.Inch.,BodyFat$BODYFAT)
## [1] 0.6135076
print("Thigh Correlation:")
## [1] "Thigh Correlation:"
plot(BodyFat$Thigh.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Thigh.Inch.,BodyFat$BODYFAT)
## [1] 0.5438656
print("Knee Correlation:")
## [1] "Knee Correlation:"
plot(BodyFat$Knee.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Knee.Inch.,BodyFat$BODYFAT)
## [1] 0.4906831
print("Ankle Correlation:")
## [1] "Ankle Correlation:"
plot(BodyFat$Ankle.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Ankle.Inch.,BodyFat$BODYFAT)
## [1] 0.2514156
print("Bicep Correlation:")
## [1] "Bicep Correlation:"
plot(BodyFat$Biceps.Inch.,BodyFat$BODYFAT)
cor(BodyFat$Biceps.Inch.,BodyFat$BODYFAT)
## [1] 0.4746496